Multiple choice

x, y, z, 25 In the sequence above, when any one of the first three terms is subtracted from the term immediately following it, the result equals x - 1. What is the value of x?

  1. 6

  2. 6.5

  3. 7

  4. 8

  5. 16
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C Correct answer
Explanation

Terms: x, y, z, 25. y-x = x-1 => y = 2x-1. z-y = x-1 => z = y+x-1 = 3x-2. 25-z = x-1 => 25-(3x-2) = x-1 => 27-3x = x-1 => 28 = 4x => x = 7.

AI explanation

Given the rule, the differences between consecutive terms are constant: (y - x) = (z - y) = (25 - z) = x - 1. This creates three equations where the sum of the three identical differences equals the overall difference between the first and last terms, meaning 3(x - 1) = 25 - x. Solving this equation yields 3x - 3 = 25 - x, which simplifies to 4x = 28. Thus, the value of x is 7.

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